This invention relates to the field of dielectric optical waveguides and optical telecommunications.
Optical waveguides guide optical signals to propagate along a preferred path or paths. Accordingly, they can be used to carry optical signal information between different locations and thus they form the basis of optical telecommunication networks. The most prevalent type of optical waveguide is an optical fiber based on index guiding. Such fibers include a core region extending along a waveguide axis and a cladding region surrounding the core about the waveguide axis and having a refractive index less than that of the core region. Because of the index-contrast, optical rays propagating substantially along the waveguide axis in the higher-index core can undergo total internal reflection (TIR) from the core-cladding interface. As a result, the optical fiber guides one or more modes of electromagnetic (EM) radiation to propagate in the core along the waveguide axis. The number of such guided modes increases with core diameter. Notably, the index-guiding mechanism precludes the presence of any cladding modes lying below the lowest-frequency guided mode. Almost all index-guided optical fibers in use commercially are silica-based in which one or both of the core and cladding are doped with impurities to produce the index contrast and generate the core-cladding interface. For example, commonly used silica optical fibers have indices of about 1.45 and index contrasts of up to about 2-3% for wavelengths in the range of 1.5 microns.
Signals traveling down an optical fiber slowly attenuate, necessitating periodic amplification and/or regeneration, typically every 50-100 km. Such amplifiers are costly, and are especially inconvenient in submarine cables where space, power sources, and maintenance are problematic. Losses for silica-based optical fibers have been driven down to about 0.2 dB/km, at which point they become limited by the Rayleigh scattering processes. Rayleigh scattering results from microscopic interactions of the light with the medium at a molecular scale and is proportional to xcfx894xcfx81, where xcfx89 is the light frequency and xcfx81 is the material density, along with some other constants of the material.
In addition to loss, signals propagating along an optical fiber may also undergo nonlinear interactions. In an ideal linear material, light does not interact with itselfxe2x80x94this is what allows a fiber to carry multiple communications channels simultaneously in separate wavelengths (wavelength-division multiplexing, or WDM), without interactions or crosstalk. Any real optical medium (even vacuum), however, possesses some nonlinear properties. Although the nonlinearities of silica and other common materials are weak, they become significant when light is propagated over long distances (hundreds or thousands of kilometers) or with high powers. Such nonlinear properties have many undesirable effects including: self/cross phase modulation (SPM/XPM), which can cause increased pulse broadening and limit bitrates; and afour-wave mixing (FWM) and stimulated Raman/Brillouin scattering (SRS/SBS), which induce crosstalk between different wavelength channels and can limit the number of achievable channels for WDM. Such nonlinearities are a physical property of the material in the waveguide and typically scale with the density of the waveguide core.
Typically, optical fibers used for long-distance communications have a core small enough to support only one fundamental mode in a desired frequency range, and therefore called xe2x80x9csingle-modexe2x80x9d fibers. Single mode operation is necessary to limit signal degradation caused by modal dispersion, which occurs when a signal can couple to multiple guided modes having different speeds. Nonetheless, the name xe2x80x9csingle-modexe2x80x9d fiber is something of a misnomer. Actually, single-mode fibers support two optical modes, consisting of the two orthogonal polarizations of light in the fiber. The existence and similarity of these two modes is the source of a problem known as polarization-mode dispersion (PMD). An ideal fiber would possess perfect rotational symmetry about its axis, in which case the two modes would behave identically (they are xe2x80x9cdegeneratexe2x80x9d) and cause no difficulties. In practice, however, real fibers have some acircularity when they are manufactured, and in addition there are environmental stresses that break the symmetry. This has two effects, both of which occur in a random and unpredictable fashion along the fiber: first, the polarization of light rotates as it propagates down the fiber; and second, the two polarizations travel at different speeds. Thus, any transmitted signal will consist of randomly varying polarizations which travel at randomly varying speeds, resulting in PMD: pulses spread out over time, and will eventually overlap unless bit rate and/or distance is limited. There are also other deleterious effects, such as polarization-dependent loss. Although there are other guided modes that have full circular symmetry, and thus are truly xe2x80x9csingletxe2x80x9d modes, such modes are not the fundamental modes and are only possible with a core large enough to support multiple modes. In conventional optical fibers, however, the PMD effects associated with the fundamental mode of a small core supporting only a xe2x80x9csingle-modexe2x80x9d are far preferable to the effects of modal dispersion in a larger core multi-mode fiber.
Another problem with directing optical signals along an optical waveguide is the presence of chromatic or group-velocity dispersion in that waveguide. Such dispersion is a measure of the degree to which different frequencies of the guided radiation propagate at different speeds (i.e., group velocities) along the waveguide axis. Because any optical pulse includes a range of frequencies, dispersion causes an optical pulse to spread in time as its different frequency components travel at different speeds. With such spreading, neighboring pulses or xe2x80x9cbitsxe2x80x9d in an optical signal may begin to overlap and thereby degrade signal detection. Thus, absent compensation, dispersion over an optical transmission length places an upper limit on the bit-rate or bandwidth of an optical signal.
Chromatic dispersion includes two contributions: material dispersion and waveguide dispersion. Material dispersion comes from the frequency-dependence of the refractive index of the material constituents of the optical waveguide. Waveguide dispersion comes from frequency-dependent changes in the spatial distribution of a guided mode. As the spatial distribution of a guided modes changes, it sample different regions of the waveguide, and therefore xe2x80x9cseesxe2x80x9d a change in the average index of the waveguide that effectively changes its group velocity. In conventional silica optical fibers, material dispersion and waveguide dispersion cancel each other out at approximately 1310 nm producing a point of zero dispersion. Silica optical fibers have also been modified to move the zero dispersion point to around 1550 nm, which corresponds to a minimum in material absorption for silica.
Unfortunately, while operating at zero dispersion minimizes pulse spreading, it also enhances nonlinear interactions in the optical fiber such as four wave mixing (FWM) because different frequencies remain phase-matched over large distances. This is particularly problematic in wavelength-division multiplexing (WDM) systems where multiple signals are carried at different wavelengths in a common optical fiber. In such WDM systems, FWM introduces cross talk between the different wavelength channels as described above. To address this problem, WDM systems transmit signals through optical fibers that introduce a sufficient dispersion to minimize cross-phase modulation, and thereafter transmits the signals through a xe2x80x9cdispersion compensating fiberxe2x80x9d (DCF), to cancel the original dispersion and minimize pulse spreading in the compensated signal. Unfortunately, aggregate interactions between the dispersion and other nonlinear processes such as self-phase modulation can complicate dispersion compensation.
Another type of waveguide fiber, one that is not based on TIR index-guiding, is a Bragg fiber, which includes multiple dielectric layers surrounding a core about a waveguide axis. The multiple layers form a cylindrical mirror that confines light to the core over a range of frequencies. The multiple layers form what is known as a photonic crystal, and the Bragg fiber is an example of a photonic crystal fiber.
Another issue in optical telecommunications system is the coupling of EM energy into, and out of, optical waveguides. Optical waveguides, such as the TIR optical fibers and photonic crystal fibers described above, support EM propagation in one or more guided xe2x80x9cmodes,xe2x80x9d which are stable EM wave patterns of the waveguide. The coupling efficiency between a given mode of a first waveguide and a given mode of a second waveguide (or some other optical component) is proportional to the degree to which the modes spatially overlap. To optimize coupling efficiency, some telecommunications system include separate mode converter modules, which receive light from a first component and alter its spatial profile of the light to improve coupling efficiency into a second component. For example, the mode converter module may include an active component such as an electronically addressable spatial light modulator.
The invention features a method for converting EM energy in one mode of a photonic crystal waveguide to another mode of the photonic crystal waveguide. Unlike the mode converter module described above, the mode conversion of the present invention takes place within a common waveguide supporting multiple guided modes. The photonic crystal waveguide includes one or more mode coupling segments that each include at least one bend in the waveguide axis. For example, the mode coupling segment may include one bend, multiple bends, a helical bend, a serpentine bend, or some combination thereof. The bend(s) in the mode coupling segment introduces a perturbation to an otherwise nominally straight waveguide, and the parameters of the bend(s) (e.g., its radius and angular extent) can be selected to cause the perturbation to couple EM energy from one guided mode to another. While the mode coupling segment corresponds to one or more bends of the waveguide along its waveguide axis, the dielectric profile cross-section of the waveguide about the waveguide axis can remain uniform. In other words, the mode conversion does not require a variation in the dielectric cross-section along the waveguide axis.
Because the EM energy can be converted between the multiple modes of the waveguide, certain modes may be used to optimize coupling into and/or out of the waveguide, while different modes may be used for propagation within the waveguide. For example, as explained further below, a particularly low-loss mode for a cylindrical Bragg fiber is TE01. However, the TE01 mode does not couple well to linearly polarized light because it has azimuthal symmetry and an electric field distribution that is maximized at a distance from the core center. Thus, by introducing a bend into the Bragg fiber having suitable parameters, linearly polarized light could be coupled into the fiber as a mode that does overlap well with linearly polarized light (e.g., the superposition of EH11 and EH1-1), and then the bend in the fiber can convert the EM energy from that first mode to the TE01 mode for subsequent propagation in the fiber. Likewise, another bend may be used to convert the EM energy from the TE01 mode to another mode when coupling the EM energy out of the fiber. Such mode conversion may be useful when, for example, the Bragg fiber is used for long-distance transmission or when, for example, it is used for dispersion compensation.
Furthermore, such mode conversion can provide specificity with respect to the polarization of the light emerging from the fiber. For example, when a bend is used to convert EM energy from the TE01 mode to the EH11 mode (or a superposition of EH11 and EH1-1) of near the output of the fiber, the light will emerge linearly polarized perpendicular to the plane of the bend. Conversely, similar polarization sensitivity applies when converting linearly polarized input light to the TE01, i.e., the bend should be oriented with respect to the direction of linear polarization. Such polarization specificity can be an advantage coupling into or from other polarization-sensitive devices. In contrast, for example, PMD in conventional optical fibers can randomize the polarization of output light.
We will now summarize different aspects, features, and advantages of the invention.
In general, in one aspect, the invention features a method for converting electromagnetic (EM) energy between guided modes of a photonic crystal waveguide having a waveguide axis. For example, the photonic crystal waveguide may be a photonic crystal fiber (e.g., a Bragg fiber). The method includes: (i) providing the photonic crystal waveguide with a mode coupling segment including at least one bend in the waveguide axis, wherein during operation the mode coupling segment converts EM energy in a first guided mode to a second guided mode over a first range of frequencies; (ii) providing EM energy in the first range of frequencies in the first guided mode of the photonic crystal waveguide; and (iii) allowing the EM energy in the first guided mode to encounter the mode coupling segment to convert at least some of the EM energy in the first guided mode to EM energy in the second guided mode.
Embodiments of the mode conversion method may include any of the following features.
Providing EM energy in the first guided mode may include coupling EM energy into the photonic crystal waveguide as the first guided mode. Furthermore, the photonic crystal waveguide may include a second mode coupling segment including at least one bend in the waveguide axis. During operation the second mode coupling segment may convert EM energy in the second guided mode to a third guided mode over the first range of frequencies, and the method may further include allowing the EM energy in the second guided mode to encounter the second mode coupling segment to convert at least some of the EM energy in the second guided mode to EM energy in the third guided mode. The method may further include coupling at least some of the EM energy in the third guided mode out of the photonic crystal waveguide. For example, the first and third guided modes are substantially similar (e.g., they may be substantially linearly polarized).
The method may further include coupling at least some of the EM energy in the second guided mode out of the photonic crystal waveguide.
The mode coupling segment may provide a conversion efficiency of the EM energy in the first guided mode to the EM energy in the second guided mode of greater than 10%, greater than 15%, greater than 25%, or greater than 50%.
The photonic crystal waveguide may have cylindrical symmetry about the waveguide axis. As a result, the guided modes may have an angular dependence that can be expressed as a linear combination of exp(imxcfx86) and exp(xe2x88x92imxcfx86), where xcfx86 is the angle in cylindrical coordinates and m is an integer and provides an angular momentum index for the guided modes. In such a case, the first and second guided modes may have angular momentum indices that differ by one. For example, one of the first and second guided modes may be a TE mode, and the other of the first and second guided modes may have a substantially linear polarization (e.g., it may be a superposition of EH1,m and EH1,xe2x88x92m or a superposition of HE1,m and HE1,xe2x88x92m).
The bend in the mode coupling segment may have a radius R and a bend angle xcex8 sufficient to convert the EM energy in the first guided mode to the EM energy in the second guided mode. For example, the mode coupling segment may include only the one bend. Furthermore, the radius R of the bend in the mode coupling segment may be substantially constant. In addition, the bend radius R may be within an order of magnitude of the absolute value of 2xcfx80(xcex94xcex212)xe2x88x921, where xcex94xcex212 is the difference in wavevector between the first guided mode and the second guided mode at a frequency in the first frequency range.
The absolute value of the difference in wavevector xcex94xcex212 between the first guided mode and the second guided mode of the EM energy at a frequency in the first frequency range may be smaller than the absolute value of the difference in wavevector xcex94xcex2lm between any other pair of the guided modes at that frequency.
The radius R of the bend in the mode coupling segment may vary along the waveguide axis.
The mode coupling segment may include a helix in the waveguide axis, the helix including the at least one bend. For example, the helix may be expressed in Cartesian coordinates as (R cos xcex8, R sinxcex8, Rxcex3xcex8), where R is the radius of the bend, xcex3 gives the rise rate of the helix in dimensionless units, and xcex8 is the azimuthal coordinate of the helix. The rise rate xcex3 may be substantially constant or it may vary. The radius of the bend R and the rise rate xcex3 can be selected based on the absolute difference in wavevector xcex94xcex212 between the first guided mode and the second guided mode at a frequency in the first frequency range. Furthermore, the photonic crystal waveguide may have cylindrical symmetry about the waveguide axis, in which case the guided modes have an angular dependence that can be expressed as a linear combination of exp(imxcfx86) and exp(xe2x88x92imxcfx86), where xcfx86 is the angle in cylindrical coordinates and m is an integer and provides an angular momentum index for the guided modes. In this case, the radius of the bend R and the rise rate xcex3 may be selected such that the absolute value of the expression xcex94xcex2lmxe2x88x92xcex94mlm(xcex3/R{square root over (1+xcex32)}) for guided modes l and m is smaller for the first and second guided modes than that for any other pair of the guided modes for a frequency in the first range of frequencies, where xcex94xcex2lm is difference in wavevector between guided modes l and m and xcex94mlm is the difference in angular momentum index for guided modes l and m.
The mode coupling segment may include a serpentine bend in the waveguide axis, the serpentine bend including the at least one bend. In particular, the serpentine bend may include multiple coplanar bends defining a varying radius of curvature for the waveguide axis in the mode coupling segment. For example, the varying radius of curvature may be oscillatory, or even periodic.
In some embodiments, the serpentine bend can be expressed as 1/R=sin(2xcfx80z/xcex9)/R0, where R is the instantaneous radius of the waveguide axis along the serpentine bend, R0 is the radius of the maximum curvature for the serpentine bend, xcex9 is the pitch of the serpentine bend, and z is the coordinate along the waveguide axis. In such cases, the radius of maximum curvature R0 and the pitch xcex9 of the serpentine bend may be selected such that the absolute value of one of the expressions xcex94xcex2lmxc2x12xcfx80/xcex9 for guided modes l and m is smaller for the first and second guided modes than that for any other pair of the guided modes for a frequency in the first range of frequencies, where xcex94xcex2lm is difference in wavevector between guided modes l and m.
The photonic crystal waveguide may have a uniform cross-section with respect to the waveguide axis.
The photonic crystal waveguide may include a dielectric confinement region surrounding the waveguide axis, and a dielectric core region extending along the waveguide axis and surrounded by the confinement region about the waveguide axis, wherein the confinement region includes a photonic crystal having at least one photonic bandgap and during operation the confinement region guides EM radiation in a first range of frequencies to propagate along the waveguide axis. For example, the average refractive index of the core may be less than 1.1 (e.g., the core may be hollow). The photonic crystal waveguide may further includes a dielectric dispersion tailoring region surrounded by the confinement region about the waveguide axis, wherein the presence of the dispersion tailoring region causes a guided core mode to form a working mode that penetrates into the dispersion tailoring region for at lease one subset of frequencies within the first range of frequencies. In any case, the confinement region may includes at least two dielectric materials having refractive indices that differ by at least 10%. Furthermore, the confinement region may include a plurality of higher index dielectric layers and a plurality of lower index dielectric layers alternating with one another to surround the core about the waveguide axis.
In an alternate description, the photonic crystal waveguide may include a dielectric core region extending along the waveguide axis, and a first set of at least three dielectric layers surrounding the core about the waveguide axis, the difference in refractive index between successive layers in the first set changing sign with each subsequent layer in the first set, wherein the first set of layers guides EM radiation in the first range of frequencies to propagate along the waveguide axis. The photonic crystal waveguide may further include at least one additional dielectric layer positioned between the core and the first set of layers, wherein the thickness of the additional dielectric layer differs from that of each of any three consecutive layers in the first set of layers by more than 10%.
The method may further include coupling at least some of the EM energy in the second guided mode out of the photonic crystal waveguide into a polarization sensitive device.
The first range of frequencies may correspond to wavelengths within the range of about 1.2 microns to 1.7 microns, or within the range of about 0.7 microns to 0.9 microns.
In general, in another aspect, the invention features a photonic crystal waveguide having multiple guided modes. For example, the photonic crystal waveguide may be a photonic crystal fiber (e.g., a Bragg fiber). The waveguide includes: (i) a dielectric confinement region surrounding a waveguide axis, the confinement region including a photonic crystal having at least one photonic bandgap, during operation the confinement region guides EM radiation in a first range of frequencies to propagate along the waveguide axis; a dielectric core region extending along the waveguide axis and surrounded by the confinement region about the waveguide axis; and (ii) a mode coupling segment including at least one bend in the waveguide axis, wherein during operation the mode coupling segment converts EM energy in a first guided mode to a second guided mode.
Embodiments of the photonic crystal waveguide having the mode coupling segment may include any of the features described above in connection with the mode conversion method.
In general, in another aspect, the invention features an optical telecommunications system including: a source module providing EM energy; and a photonic crystal waveguide coupled to the source module and having a waveguide axis, the photonic crystal waveguide having a mode coupling segment including at least one bend in the waveguide axis, wherein during operation the mode coupling segment converts EM energy in a first guided mode derived from the source module to a second guided mode for a first range of frequencies.
Embodiments of the telecommunications system may include any of the features described above in connection with the mode conversion method.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. In case of conflict with any publications, patent applications, patents, and other references incorporated herein by reference, the present specification, including definitions, will control. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting.
Additional features, objects, and advantages of the invention will be apparent from the following detailed description and drawings, and from the claims.